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A toy rocket was launched from the ground. The function f(x) = -16x^2 + 192x shows the height of the rocket f(x), in feet, from the ground at time x seconds. What is the axis of symmetry of the graph of f(x), and what does it represent? x = 12; it takes 12 seconds to reach the maximum height and 12 seconds to fall back to the ground x = 12; it takes 12 seconds to reach the maximum height and 24 seconds to fall back to the ground x = 6; it takes 6 seconds to reach the maximum height and 6 seconds to fall back to the ground x = 6; it takes 6 seconds to reach the maximum height and 3 seconds to fall back to the ground
I think its either C or D
i think it is not a 100% sure though
can you help me with a couple more?
yeah i will try
Functions f(x) and g(x) are shown below: f(x) = x2 g(x) = x2 + 10x + 25 In which direction and by how many units should f(x) be shifted to obtain g(x)? Right by 5 units Left by 5 units Right by 10 units Left by 10 units
hint: (x^2 + 10x + 25) = (x+5)^2
so would it be D?
nope, please look carefully at what I wrote (x+k)^2 moves the graph x^2 to the left k units
yes, B is the answer, but do you understand how to get (x+5)^2?
can you explain it a little, I sort of forgot.
have you seen this formula? (a+b)^2 = a^2 + 2ab + b^2?
great! in the equation x^2 + 10x + 25, do you see how x = a and b = 5? when you plug in x for a and b for 5, do you see how x^2 + 10x + 25 = (x+5)^2? this is called "factoring", basically you want to find a and b so you can simplify x^2 + 10x + 25 into (x+5)^2
oh, I remember thanks!
do you mind helping me with a couple more?
sure, I guess
The steps to derive the quadratic formula are shown below: Which of the following statements best describes the first incorrect step? In Step 4, square of quantity of b over 2 times a instead of b over 2 times a was added on both sides. In Step 5, x plus b over 2 times a, all squared was written instead of x plus b over 4a, all square. In Step 6, c over a was written instead of -c over a inside the root. In Step 7, square of quantity of b over 2 times a was written instead of b over 2 times a inside the root.
NOTE: I got this from a website, I didn't write this out myself, but these are the steps to derive the quadratic equation
David kicks a soccer ball off the ground and in the air, with an initial velocity of 35 feet per second. Using the formula H(t) = -16t2 + vt + s, what is the maximum height the soccer ball reaches?
for this one I know you plug in the 35 for v but what do you plug in for s?
v = initial velocity = 35, s = initial height = 0
an object on the ground has a height of 0
initial height = 0, because the ball is on the ground
ok I can do this one by myself
can you help me with 3 more?
Water coming out from a fountain is modeled by the function f(x) = -x2 + 7x + 5 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f(x) from x = 4 to x = 6 represent? The water falls down with an average speed of 5 feet per second from 4 seconds to 6 seconds. The water falls down with an average speed of 3 feet per second from 4 seconds to 6 seconds. The water travels an average distance of 5 feet from 4 seconds to 6 seconds. The water travels an average distance of 3 feet from 4 seconds to 6 seconds.
If 5p = -100 + 3Q2, which of the following could Q possibly be? Q = square root of 5p-100/ 3 Q = square root of 5p+100/3 Q = square root of -5p+100/ 3 Q = square root of -5p-100/ 3
this one is a bit tough to explain but I'll try average rate of change = speed = distance/time the average rate of change between x = 6 seconds and x = 4 seconds = distance travelled between 4 to 6 seconds/(6-4 seconds) = [f(6)-f(4)]/(6-4)
and for the second one: 5p = -100 + 3Q^2 all you're doing is solving for Q in terms of p add 100 to each side divide each side by 3 take the square root of each side to find Q
35p=q^2 I got 5.9160797830996160425673282915616 when I did the square root of 35
??? I think you're confused, can I try outlining it step by step?
sorry I got confused I understand now.
the answer I got is B
yup! good job
I have one more. Do you think you can help me?
are there any x values that don't have y values?